On monomorphisms of hypergraphic automata
https://doi.org/10.26907/2949-3919.2024.3.63-75
Abstract
Hypergraphic automata are automata, state sets and output symbol sets of which are hypergraphs, being invariant under actions of transition and output functions. Universally attracting objects in the category of hypergraphic automata are called universal hypergraphic automata. The semigroups of input symbols of such automata are derivative algebras of mappings for such automata. So their properties are interconnected with properties of the algebraic structures of the automata. This paper describes the structure of monomorphisms of such automata and their semigroups of input signals.
About the Author
E. V. Khvorostukhina
Yuri Gagarin State Technical University of Saratov
Russian Federation
Ekaterina Vladimirovna Khvorostukhina
Russian Federation
Ekaterina Vladimirovna Khvorostukhina
77 Politechnicheskaya str., Saratov 410054
References
1. B.I. Plotkin, L.Ja. Geenglaz, А.А. Gvaramija, Algebraic structures in automata and databases theory, World Scientific Publishing Co., River Edge, NJ, 1992. DOI: https://doi.org/10.1142/1631
2. V.A. Molchanov, E.V. Khvorostukhina, On problem of abstract definability of universal hypergraphic automata by input symbol semigroup, Chebyshevskii Sb. 20 (2), 259–272 (2019) [in Russian]. DOI: https://doi.org/10.22405/2226-8383-2019-20-2-259-272
3. E.V. Khvorostukhina, V.A. Molchanov, On problem of concrete characterization of universal automata, Lobachevskii J. Math. 38 (4), 664–669 (2017). DOI: https://doi.org/10.1134/S1995080217040114
4. E.V. Khvorostukhina, V.A. Molchanov, Abstract characterization of input symbol semigroups of universal hypergraphic automata, Lobachevskii J. Math. 41 (2), 214–226 (2020). DOI: https://doi.org/10.1134/S1995080220020109
5. V.A. Molchanov, E.V. Khvorostukhina, On problem of abstract characterization of universal hypergraphic automata, Izv. Saratov Univ. Math. Mech. Inform. 17 (2), 148– 159 (2017) [in Russian]. DOI: https://doi.org/10.18500/1816-9791-2017-17-2-148-159
6. E.V. Khvorostukhina, On monomorphisms of hypergraphic automata, The international conference “Algebra and mathematical logic: theory and applications” dedicated to the 130-th birthday of the founder of the department of algebra of Kazan university, professor N.G. Chebotarev, and the 80-th birthday of the chair of the department professor M.M. Arslanov, 177–179 (2024) [in Russian].
7. A.I. Mal’cev, Algebraic Systems, Springer-Verlag, Berlin, New York, 1973. DOI: https://doi.org/10.1007/978-3-642-65374-2
8. G. Lallement, Semigroups and combinatorial applications, John Wiley & Sons, New York– Chichester–Brisbane, 1979.
9. V.V. Vagner, The theory of relations and the algebra of partial mappings, in: “The theory of semigroups and their applications” 1, 3–178, (1965) [in Russian].
10. A. Bretto, Hypergraph theory. An introduction, Springer, Cham, 2013. DOI: https://doi.org/10.1007/978-3-319-00080-0
11. F. Ka´rteszi, Introduction to finite geometries, North Holland, Hungary, 2014.
Review
For citations:
Khvorostukhina E.V. On monomorphisms of hypergraphic automata. Mathematics and Theoretical Computer Science. 2024;2(3):63-75. (In Russ.) https://doi.org/10.26907/2949-3919.2024.3.63-75
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